The present invention relates to the recording and reproduction of binary data in magnetic disk storage systems for digital computers, particularly to a magnetic disk storage system employing a non-linear transducer (e.g., a magneto-resistive (MR) read head) adjusted to operate in a non-linear region but with higher gain, together with a non-linear correction circuit for attenuating the non-linearity in the read signal.
Computer systems typically comprise a disk storage device, for example a magnetic or optical disk drive, which provide an inexpensive means to store large amounts of digital data in a non-volatile manner. The disk storage device is essentially a communication system where the storage medium (magnetic or optical), transducer, and read/write electronics constitute the communication channel. Similar to other communication channels, the digital data in storage devices is xe2x80x9ctransmittedxe2x80x9d through the channel by modulating an analog signal. In magnetic disk storage systems, for example, the digital data modulates the current in an inductive write coil in order to write a sequence of magnetic transitions onto the surface of a magnetic disk in concentric, radially spaced tracks. And in optical disk storage systems, the digital data may modulate the intensity of a laser beam in order to write a series of xe2x80x9cpitsxe2x80x9d onto the surface of an optical disk in tracks that spiral inward toward the center of the disk.
During a read operation, a transducer or read head is positioned in close proximity to the surface of the disk, and while the disk spins under the read head, the read head senses the alterations (magnetic or optical) representing the digital data. The read head generates an analog read signal comprising pulses induced by the surface alterations. In magnetic recording, for example, the read head comprises a sensor that is responsive to the changes in the magnetic flux caused by the magnetic transitions representing the digital data. The two main types of magnetic sensors employed in magnetic storage devices include the conventional inductive coil read head which is sensitive to the change in magnetic flux, and the more recent magneto-resistive (MR) read head comprising a resistive element which is sensitive to the strength or magnitude of the magnetic flux. Both sensors generate an analog read signal comprising pulses induced by the magnetic transitions, but the MR read head exhibits substantially higher sensitivity and noise immunity which is why they are displacing the older inductive coil type read heads.
As with other bandlimitted communication channels, the maximum capacity of a disk storage system is approximated by Shannon""s equation for the capacity of an additive white Gaussian noise channel:   C  =      W    ⁢          xe2x80x83        ⁢                  log        ⁢                  (                      1            +                          P                                                N                  0                                ⁢                W                                              )                    .      
In the above equation, W is the channel bandwidth, N0 is the noise power spectrum, and P is the signal power. The bandwidth W of a disk storage system is, for the most part, limited by the characteristics of the storage medium. Thus, once the storage medium is chosen, the maximum capacity of the storage system is essentially a function of the signal power P and the noise power N0 (i.e., the signal-to-noise ratio or SNR). Certain characteristics of the storage medium also contribute to the noise power in the read signal, so designers generally choose the least expensive medium that will provide the highest bandwidth and SNR to attain maximum storage capacity.
In addition to innovations in the storage medium itself, attempts to increase storage capacity generally focus on improving the actual SNR through improvements to the transducer and drive electronics, as well as improving the effective SNR through the use of error correction codes (ECC), such as the Reed-Solomon ECC codes, and through the use of sophisticated signal processing techniques spawned by communication theory.
One such advancement in communication theory that has recently been applied to disk storage systems to achieve significant gains in storage capacity is partial response (PR) signaling with maximum likelihood (ML) sequence detection. Partial response signaling refers to a particular method for transmitting symbols represented as analog pulses through a communication medium. The benefit is that at the signaling instances (baud rate) there is no intersymbol interference (ISI) from other pulses except for a controlled amount from immediately adjacent, overlapping pulses. Allowing the pulses to overlap in a controlled manner leads to an increase in the symbol rate (linear recording density) without sacrificing performance in terms of SNR. Stated differently, a partial response signal provides an increase in the effective SNR by making more efficient use of the channel bandwidth.
Partial response channels are characterized by the polynomials
(1xe2x88x92D)(1+D)n
where D represents a delay of one symbol period and n is an integer. For n=1, 2, 3, the partial response channels are referred to as PR4, EPR4 and EEPR4, with their respective frequency responses shown in FIG. 1A. The channel""s dipulse response, the response to an isolated symbol, characterizes the transfer function of the system (the output for a given input). With a binary xe2x80x9c1xe2x80x9d bit modulating a positive dipulse response and a binary xe2x80x9c0xe2x80x9d bit modulating a negative dipulse response, the output of the channel is a linear combination of time shifted dipulse responses
y(t)=xcexa3anp(txe2x88x92nT)
where an denotes the write current symbols +1 and xe2x88x921 at time n and p(t) represents the channel""s dipulse response shifted by nT (n symbol periods). The dipulse response for a PR4 channel (1xe2x88x92D2) is shown as a solid line in FIG. 1B. Notice that at the symbol instances (baud rate), the dipulse response is zero except at times t=0 and t=2. Thus, the linear combination of time shifted PR4 dipulse responses will result in zero ISI at the symbol instances except where immediately adjacent pulses overlap.
It should be apparent that the linear combination of time shifted PR4 dipulse responses will result in a channel output of +2, 0, or xe2x88x922 at the symbol instances (with the dipulse samples normalized to +1, 0, xe2x88x921) depending on the binary input sequence. The output of the channel can therefore be characterized as a state machine driven by the binary input sequence, and conversely, the input sequence can be estimated or demodulated by running the signal samples at the output of the channel through an xe2x80x9cinversexe2x80x9d state machine. Because noise will obfuscate the signal samples, the inverse state machine is actually implemented as a trellis sequence detector which computes a most likely input sequence associated with the signal samples. The algorithm for selecting a most likely sequence through a trellis was invented by a man named Viterbi, and thus the algorithm is commonly referred to as the Viterbi algorithm.
The Viterbi algorithm for a PR4 trellis sequence detector is understood from its state transition diagram shown in FIG. 2A. Each state 2 is represented by the last two input symbols (in NRZ after preceding), and each branch from one state to another is labeled with the current input symbol in NRZ 4 and the corresponding sample value 6 it will produce during readback. The demodulation process of the PR4 sequence detector is understood by representing the state transition diagram of FIG. 2A as a trellis diagram shown in FIG. 2B. The trellis diagram represents a time sequence of sample values and the possible recorded input sequences that could have produced the sample sequence. For each possible input sequence, an error metric is computed relative to a difference between the sequence of expected sample values that would have been generated in a noiseless system and the actual sample values output by the channel. For instance, a Euclidean metric is computed as the accumulated square difference between the expected and actual sample values. The input sequence that generates the smallest Euclidean metric is the most likely sequence to have created the actual sample values; this sequence is therefore selected as the output of the sequence detector.
To facilitate the demodulation process, the sequence detector comprises path memories for storing each of the possible input sequences and a corresponding metric. A well known property of the sequence detector is that the paths storing the possible input sequences will xe2x80x9cmergexe2x80x9d into a most likely input sequence after a certain number of sample values are processed, as long as the input sequence is appropriately constrained. In fact, the maximum number of path memories needed equals the number of states in the trellis diagram; the most likely input sequence will always be represented by one of these paths, and these paths will eventually merge into one path (i.e., the most likely input sequence) after a certain number of sample values are processed.
The xe2x80x9cmergingxe2x80x9d of path memories is understood from the trellis diagram of FIG. 2B where the xe2x80x9csurvivorxe2x80x9d sequences are represented as solid lines. Notice that each state in the trellis diagram can be reached from one of two states; that is, there are two transition branches leading to each state. With each new sample value, the Viterbi algorithm recursively computes a new error metric and retains a single survivor sequence for each state corresponding to the minimum error metric. In other words, the Viterbi algorithm will select one of the two input branches into each state since only one of the branches will correspond to the minimum error metric, and the paths through the trellis corresponding to the branches not selected will merge into the paths that were selected. Eventually, all of the survivor sequences will merge into one path through the trellis which represents the most likely estimated data sequence to have generated the sample values as shown in FIG. 2B.
The performance of the trellis sequence detector in terms of bit error rate depends on the amount of noise in the system, including noise due to the spectrum of the read signal diverging from the ideal partial response. Linear distortions in the read signal can generally be suppressed using a linear equalizer which may operate on the continuous-time analog read signal or the discrete-time samples of the read signal. Typical read channels employ both an analog equalizer, such as a biquad analog filter, followed by a nth order finite-impulse response (FIR) discrete-time filter. Linear equalizers, however, are not effective in attenuating non-linear distortions in the read signal, such as asymmetries caused by the non-linear response of a magneto-resistive (MR) read head.
An MR read head comprises an MR sensor element with a resistance which is proportional to the strength of the magnetic flux; the read signal is generated by applying a current to the MR element and measuring the voltage across it as it passes over the magnetic transitions recorded on the disk. FIG. 3 is a plot of the head""s resistance versus the magnetic flux which illustrates that the response can be very non-linear. The effect of this non-linearity on the read signal generally results in pulses that are not symmetric, for example, the magnitude of a pulse induced by a positive magnetic transition may be greater than the magnitude of a pulse induced by a negative magnetic transition (note that the asymmetry in the pulses may be reversed, and other asymmetries may also be present in the read signal). Ultimately, the non-linear distortions prevent the read signal from attaining the desired partial response target, introducing noise into the sample values which degrades the performance of the trellis sequence detector.
The undesirable non-linear characteristic of an MR read head has been ameliorated in prior art techniques by applying a magnetic biasing field across the MR element so that it operates in a linear region of the response while still providing sufficient sensitivity and stability. This is illustrated in FIG. 3 which shows that the prior art solution is to bias the MR sensor so that it operates near a linear region of its response. However, the linear region of the MR response may not be the region of highest gain, and therefore not necessarily the optimum operating region.
There is, therefore, a need for an improved sampled amplitude read channel for use in magnetic disk storage systems that provides a performance enhancing improvement by adjusting a non-linear read head to attain optimum sensitivity. In particular, it is an object of the present invention to optimize the operation of an MR read head to improve the performance and increase the capacity of a magnetic disk storage system.
A sampled amplitude read channel is disclosed for magnetic disk storage systems utilizing a read head exhibiting a non-linear response, such as a magneto-resistive (MR) read head. A sensor of the read head is adjusted to operate in a region of its response that provides optimum gain even though it may be a region of higher non-linearity. To compensate for the non-linearity introduced into the read signal, the read channel further comprises an adaptive non-linear correction circuit that is tuned to achieve the best overall performance. The analog read signal is sampled and the discrete time samples equalized into a desired partial response prior to sequence detection. The non-linear correction circuit is inserted into the read path prior to the sequence detector in order to attenuate the non-linear distortions that would otherwise degrade the performance of the sequence detector. A channel quality circuit integrated into the read channel measures and accumulates a predetermined error metric, such as a squared sample error or a bit error, that is used to optimize the adjustment of the sensor in the read head. By iteratively adjusting the sensor and tuning the non-linear correction circuit, an optimum sensor setting that minimizes the accumulated error metric is determined, saved, and then used as the operating setting during normal operation of the magnetic disk storage system.